Dear Phil and dear gap forum
I have a finitely presented group G, generated by x_1, ..., x_n,
and would like to know the order of x_i (i = 1,...,n) in the abelianization
i.e. the order of phi(x_i), where phi: G ->
What is the best way to this in GAP?
I don't know the best way, but I can try to suggest one way that I would
try. You can compute the quotient of class 1 of your group G with the ANU
Nilpotent Quotient Algorithm, (see
http://www.mathematik.tu-darmstadt.de/~nickel/software/index.html ) so
that you get a polycyclic presented group, in which you can easily
calculate the orders of the elements.